The muon is a subatomic particle that includes the positive and negative muon with a charge of 1 and 1, respectively. For the mass, the muon is heavier than the electron. As for a proton beam, the muon beam shows a Bragg peak when it interacts with materials. Therefore, the muon beam, as well as the proton beam, can also be considered as a candidate for radiotherapy. In this study, based on the Monte Carlo method, we defined a water phantom that which included a target volume and three interesting volumes. Then, the interaction processes of proton, positive and negative muon beams in materials were simulated. Moreover, the dose depositions of proton beam, positive and negative muon beams in each volume were calculated. An analysis of the calculated results, showed that compared to a proton beam, especially the negative muon beam, had an advantage in reducing the physical dose deposition in the upstream volume of the target.